We know that the first order Marcum Q-function can be represented as $$Q_1(a, b)=\int_{b}^{\infty} t \exp{(-(t^2+a^2)/2)} I_0(a t) \, dt ,$$ I am trying to compute the following integral $A$ and $B$: $$A=\int_0^{\infty} xg(x) dx$$, $$B=\int_0^{\infty} x^2g(x) dx$$ where $$g(x)=G'(x) $$ and $$G(x)= Q_1(\frac{v_1}{\sigma_1},\frac{x}{\sigma_1})Q_1(\frac{v_2}{\sigma_2},\frac{x}{\sigma_2}) $$
Thank you for your time and kindness.
With respect.